A new, robust and resistant, inversion based 2D Fourier transformation is presented where the spectrum is discretized by series expansion (S-IRLS-FT) using Hermite-functions as basis functions. The series expansion coefficients are given by the solution of a linear inverse problem. Taking advantage of the beneficial properties of Hermite-functions, that they are the eigenfunctions of the inverse Fourier transformation, the elements of the Jacobian matrix can be calculated fast and easily, without integration. The procedure can be robustified using Iteratively Reweighted Least Squares (IRLS) method with Steiner weights. This results in a very efficient robust and resistant inversion procedure. Its applicability is demonstrated in the reduction to the pole of magnetic data set measured in regular (equidistant sampling) and “random walk” measurement arrays.


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  1. Dobróka, M., Szegedi, H., Somogyi Molnár, J. Szűcs, P.
    [2015] On the Reduced Noise Sensitivity of a New Fourier Transformation Algorithm. Math. Geos. 47:(6) pp. 679–697.
    [Google Scholar]
  2. DobrokaM, SzegediH, and VassP.
    [2017] Inversion-based Fourier transform as a new tool for noise rejection, INTECH 2017, DOI:10.5772/66338
    https://doi.org/10.5772/66338 [Google Scholar]
  3. Gyulai, Á., Szabó, N. P.
    [2014] Series expansion based geoelectric inversion methodology used for geo-environmental investigations. Frontiers in Geosc. 2:(1) pp. 11–17.
    [Google Scholar]
  4. Kunaratnam, K.
    [1981] Simplified expressions for the magnetic anomalies due to vertical rectangular prisms. Geophys. Prosp. 29. pp. 883–890.
    [Google Scholar]
  5. Steiner, F.
    [1997] Optimum methods in statistics. Akadémiai Kiadó, Budapest.
    [Google Scholar]
  6. Szegedi, H., Dobróka, M.
    [2014] On the use of Steiner’s weights in inversion-based Fourier transformation - robustification of a previously published algorithm. Acta Geodaetica et Geophysica, 49/1, 95–104, DOI 10.1007/s40328‑014‑0041‑0.
    https://doi.org/10.1007/s40328-014-0041-0 [Google Scholar]

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